Simplify a combination

  • Thread starter Aleoa
  • Start date
  • #1
128
5
Member has been warned not to delete the template.
I'm trying to simplify the combination defined as : [itex]\binom{n}{\frac{n}{2}}[/itex].

I did some calculations, starting from the factorial formula [itex]\frac{n!}{(\frac{n}{2})!(\frac{n}{2})!}[/itex] and i found this form :

[itex]2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})...[/itex]

but i don't know how to continue, can you help me ?
 

Answers and Replies

  • #2
14,413
11,726
but i don't know how to continue, can you help me ?
No, since you haven't said what your goal is. To me ##\binom{n}{\frac{n}{2}}## is already fine.
 
  • #3
128
5
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support
 
  • #4
14,413
11,726
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support
In this case I'd try where Stirling's approximation would get me.
 
  • #5
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support
As fresh_42 suggested, use Stirling's formula. Every student of probability should be thoroughly familiar with that formula, as it is used everywhere.
 

Related Threads on Simplify a combination

  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
792
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
5
Views
571
  • Last Post
Replies
2
Views
805
  • Last Post
Replies
1
Views
2K
Top